Remainder Homework

When my students have had the opportunity to work through the Warm Up, I ask them to discuss the pattern that emerged with the people at their table.  While students work together, I circulate to determine the order in which the tables will present their ideas. My goal for this discussion is to help my students develop a strong conceptual understanding of the idea expressed in the Remainder Theorem.  For this reason, I structure the discussion so that the core idea is introduced first and we build towards the formal mathematical notation [MP3]. To keep the conversation moving in this direction, I use phrases like

  • Can you build on what <Student> has shared?
  • Is there any part of what <Student> has said that you disagree with? 
  • Can you express that idea more formally?
  • Do you see a connection between ___ and ___?

When I am satisfied that my students have a good conceptual understanding of the Remainder Theorem, we take some formal notes with examples.  Examples focus on using the Remainder theorem to identify one root of a polynomial, divide it out of the polynomial expression and then factor the remaining polynomial.  The guided practice that follows the discussion will provide additional reinforcement on this process.

Although many teachers take time at this point in the curriculum to teach students synthetic division and synthetic substitution I do not.  Although this algorithm saves students a bit of time in performing long division of specialized cases, it is not specifically called for in the CCSS. Furthermore, students do not have the mathematical background to understand why it works and therefore think of it as a process to memorize.  I feel time is much better spent in developing the conceptual understanding of the Remainder Theorem.  


Внутренний голос подсказывал ей, что лучше всего было бы дождаться звонка Дэвида использовать его ключ, но она понимала, что он может его и не найти. Сьюзан задумалась о том, почему он задерживается так долго, но ей пришлось забыть о тревоге за него и двигаться вслед за шефом.

Стратмор бесшумно спускался по ступенькам. Незачем настораживать Хейла, давать ему знать, что они идут. Почти уже спустившись, Стратмор остановился, нащупывая последнюю ступеньку.

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